TY - JOUR

T1 - Analysis of a tripartite entanglement distribution switch

AU - Nain, Philippe

AU - Vardoyan, Gayane

AU - Guha, Saikat

AU - Towsley, Don

PY - 2022

Y1 - 2022

N2 - We study a quantum switch that distributes tripartite entangled states to sets of users. The entanglement switching process requires two steps: First, each user attempts to generate bipartite entanglement between itself and the switch, and second, the switch performs local operations and a measurement to create multipartite entanglement for a set of three users. In this work, we study a simple variant of this system, wherein the switch has infinite memory and the links that connect the users to the switch are identical. This problem formulation is of interest to several distributed quantum applications, while the technical aspects of this work result in new contributions within queueing theory. The state of the system is modeled as continuous-time Markov chain (CTMC), and performance metrics of interest (probability of an empty system, switch capacity, expectation, and variance of the number of qubit-pairs stored) are computed via the solution of a two-dimensional functional equation obtained by reducing it to a boundary value problem on a closed curve. This work is a follow-up of Nain et al. (Proc ACM Measure Anal Comput Syst(POMACS) 4, 2020) where a switch distributing entangled multipartite states to sets of users was studied, but only the switch capacity and the expected number of stored qubits were derived.

AB - We study a quantum switch that distributes tripartite entangled states to sets of users. The entanglement switching process requires two steps: First, each user attempts to generate bipartite entanglement between itself and the switch, and second, the switch performs local operations and a measurement to create multipartite entanglement for a set of three users. In this work, we study a simple variant of this system, wherein the switch has infinite memory and the links that connect the users to the switch are identical. This problem formulation is of interest to several distributed quantum applications, while the technical aspects of this work result in new contributions within queueing theory. The state of the system is modeled as continuous-time Markov chain (CTMC), and performance metrics of interest (probability of an empty system, switch capacity, expectation, and variance of the number of qubit-pairs stored) are computed via the solution of a two-dimensional functional equation obtained by reducing it to a boundary value problem on a closed curve. This work is a follow-up of Nain et al. (Proc ACM Measure Anal Comput Syst(POMACS) 4, 2020) where a switch distributing entangled multipartite states to sets of users was studied, but only the switch capacity and the expected number of stored qubits were derived.

KW - Boundary value problem

KW - Markov process

KW - Quantum switch

KW - Queueing

UR - http://www.scopus.com/inward/record.url?scp=85123208138&partnerID=8YFLogxK

U2 - 10.1007/s11134-021-09731-w

DO - 10.1007/s11134-021-09731-w

M3 - Article

AN - SCOPUS:85123208138

VL - 101

SP - 291

EP - 328

JO - Queueing Systems: theory and applications

JF - Queueing Systems: theory and applications

SN - 0257-0130

IS - 3-4

ER -